4 Answers
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First of all, we should keep in mind that präteritum is normally not used in spoken german.

Having said that, let´s break it into pieces.

1) "I didn't see her".

Teoretically, Perfekt Partizip should suffice here, but there is a fact that we must take into account, something happens (happened) after the subject (I) "didn´t see her", so we should use another form of past that lets us describe an event in the past and another event that came short after, that is Plusquamperfekt, which is built with the verb in Partizip II and "haben" or "sein" (depending on how the verb builds its Perfekt) in Präteritum.

Our posibilities would then be:

ich sah sie nicht. (Präteritum)

ich habe sie nicht gesehen. (Perfekt)

ich hatte sie nicht gesehen. ( Plusquamperfekt, chosen )

2) "and when I realized it was her" or "and when i realized that it was her".

Now we should talk about the event that came after what we just formulated in "far" past, but we talk about it in "near" past ( Perfekt Partizip ).

und als ich bemerkt habe, (Perfekt)

Now for the "that it was her" part, we try first to use Perfekt Partizip, but since the main verb is "sein", and "sein" is a modal verb, we use Präteritum instead of Perfekt.